3. The Dynamic-Atmosphere Energy-Transport (DAET) Inverse Modelling Study
of MY29 Data.Climate Science is built on a conceptual model that removes from its fundamental analysis the dual complementary energy environments of a lit daytime hemisphere and a dark nighttime hemisphere. By preserving these two energy environments the Dynamic-Atmosphere Energy Transport (DAET) climate model more appropriately mimics the meteorological reality of a solar lit globe [30] and the DAET model is therefore applied herein.
3.1 The Vacuum Planet Equation (VPE).
Studies of the atmospheric dynamics of terrestrial solar system planets has a long and detailed history. The fundamental equation for the basis of this work is exemplified by the radiation balance equation (corrected from the published error pers comm) used by Sagan and Chyba [15]: -
Equation 1:
Te ≡ [S π R2(1-A)/4 π R2 ε σ]1/4where σ is the Stefan-Boltzmann Constant (S-B), ε the effective surface emissivity, A the wavelength-integrated Bond albedo, R the planet's (or moon’s) radius (in metres), and S the solar constant (in Watts/m2) at the planet's (or moon’s) average orbital distance from the sun.” [15] Equation 1 is hereafter called the Vacuum Planet Equation (VPE).
The Absorptance
α of the surface of a material is its effectiveness in absorbing radiant energy. Absorptance is the ratio of the absorbed to the incident radiant power.
The Reflectance ρ of the surface of a material is a measure of its capability to reflect radiant energy. Reflectance is defined as the fraction of incident radiation reflected by a surface or discontinuity.
For an incident beam of unit power striking a material surface the Absorptance α plus Reflectance ρ is unity because energy is conserved.
Equation 2: α + ρ =1.
Emittance ε is the ratio of radiant exitance of a thermal radiator to that of a full radiator (black-body) at the same temperature. As such Emittance ε is the low-frequency radiant converse of Absorptance α and is less than unity because of the missing component of energy lost to the absorbing surface by Reflectance ρ. For a surface at thermal radiant equilibrium the amount of insolation energy absorbed is equal to the amount of thermal radiant energy emitted, therefore ε = α and consequently Kirchhoff’s Law applies [31]:
As a material body with zero reflectance would be a black-body (Kirchhoff’s Law of Thermal Radiation) and the surface is in fact a grey-body it follows therefore that reflectance must be included in the computation of the total energy budget.
3.3 The role of Bond Albedo (A) in the Atmospheric Energy Budget.
In equation 1 the wavelength-integrated Bond Albedo A reduces the power of the solar irradiance that acts within the planetary climate system. The Bond Albedo is a bypass filter that records the planetary brightness and removes from the climate budget the solar energy flux that exits the planetary atmosphere and returns to space as unaltered high frequency radiation.
Therefore, it is axiomatic that all the high frequency energy flux post-albedo (1-A) is degraded to low frequency thermal radiant flux by the processes of light interception, both in the planet’s atmosphere and at the physical surface. For the planet Mars there are three main processes that capture insolation energy. These are:
1. Atmospheric dust which generates the visibility obscuring haze, warms the atmosphere and so reduces the power of the insolation that reaches the surface [32].
2. The physical surface which absorbs insolation energy by absorptance α.
3. The action of surface reflectance ρ that creates a process of near surface backlighting of the dust in the boundary layer of the lower atmosphere.
N.B. Although the Martian surface is obviously visible, this lit surface reflectance of insolation is of necessity already incorporated into the Bond Albedo (AM). Consequently, the insolation energy rejected by the surface {(1-AM)*ρ} must be absorbed by the atmosphere, otherwise the black body status for the thermal emission temperature of the planetary globe that is demonstrated by setting the emissivity to value 1 in the Vacuum Planet Equation could never be achieved (Table 7).
3.4 Global Average Temperature Calculations.
The Black-body temperature Te for Mars is 209.8 Kelvin, this value is achieved by setting the emissivity ε to unity in the VPE (Equation 1), however the observed mean surface temperature for this planet is Ts = 211.8 K (this study) therefore the difference Δ T between Te and Ts = 2.0 Kelvin which is the atmospheric thermal enhancement effect for Mars. (Table 7).
Emissivity is an intrinsic property of the material composition of the planetary surface of Mars, and as such surface emissivity is independent of the nature and presence of an overlying atmosphere. When the surface emissivity is set to unity this parameter adjustment includes in the VPE the missing component of high frequency reflectance energy that must have been absorbed by the atmosphere.
Clearly for Mars the 0.25 Bond Albedo, which is applied for the process of insolation energy filtering, must already incorporate into its value any planetary surface reflectance of insolation that is lost to space. Consequently, the post-albedo insolation energy flux (1-AM) that illuminates the surface must all be captured by atmospheric opacity and converted into thermal energy for use within the dynamics of the Martian climate system.